Trailing 4-2 in the fifth, the Phillies scored three times to forge ahead for good.
Phillies starter Roy Halladay (11-8) and Jimmy Rollins each singled to lead off the frame against Ricky Nolasco (12-13). Both moved up on Juan Pierre's sacrifice and scored when Utley grounded an 0-1 pitch up the middle, forging a 4-4 tie.
Brown followed by smashing a one-hopper off the right-center field wall for a go-ahead triple.
Halladay went five innings to get the win, giving up four runs on six hits. He walked three and fanned seven.
Nolasco was tagged for five runs on nine hits through five frames.
Giancarlo Stanton went 3-for-4 with a solo homer and three RBI for the Marlins.